In many applications, particularly in optics, for example in microscopy, large sets of image data accrue. One possibility to compress image data of such a type consists in the application of a biorthogonal filter bank to the respective images, followed by a compression of the result, for example omitting elements that are equal to zero (or, where appropriate, close to zero). A special case of such a filter bank of this is so-called wavelet decomposition, which will be elucidated in more detail later.
For the purpose of processing images of such a type, convolution and deconvolution operations are frequently used, whereby deconvolution operations may be represented iteratively by convolutions. For example, a recorded image represents a convolution between an image component that has its origin solely in a recorded object and a point spread function (PSF) of an image-recording device being used, which essentially describes how a discrete point is imaged and consequently describes the behaviour of the image-recording device being used. By virtue of an appropriate deconvolution, the influence of the image-recording device can be removed by computation, and consequently the quality of the image can be enhanced.
Accordingly, it is desirable to provide possibilities by which convolution operations of such a type with filtered and/or compressed image data, in particular with wavelet-decomposed image data, can be carried out. Appropriate methods are known, for example, from P. P. Vaidyanathan, “Orthonormal and biorthonormal filter banks as convolvers, and convolutional coding gain”, IEEE Trans. Signal Processing, Vol. 41, pages 2110-2130, June 1993, and Iddo Drori, Dani Lischinski, “Fast Multiresolution Image Operations in the Wavelet Domain”, IEEE Transactions on Visualization and Computer Graphics, Vol. 09, No. 3, pages 395-411, July-September 2003. With the algorithms described therein, however, the result of the convolution is present in the local space, i.e. not in wavelet-decomposed form, and consequently, in particular, in uncompressed form, so that subsequently with a view to compressed storage a filtering, in particular a wavelet decomposition, again has to be performed, which requires a corresponding computing capacity.
Therefore, there is a need for methods and apparatuses with which an image processing of such a type, in particular the application of convolution operations, is possible in efficient manner.